Minimizing the Expected Market Time to Reach a Certain Wealth Level
AbstractIn a financial market model, we consider variations of the problem of minimizing the expected time to upcross a certain wealth level. For exponential Levy markets, we show the asymptotic optimality of the growth-optimal portfolio for the above problem and obtain tight bounds for the value function for any wealth level. In an Ito market, we employ the concept of market time, which is a clock that runs according to the underlying market growth. We show the optimality of the growth-optimal portfolio for minimizing the expected market time to reach any wealth level. This reveals a general definition of market time which can be useful from an investor?s point of view. We utilize this last definition to extend the previous results in a general semimartingale setting.
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Bibliographic InfoPaper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 230.
Date of creation: 01 Aug 2008
Date of revision:
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Numeraire portfolio; growth-optimal portfolio; market time; upcrossing; overshoot; exponential Levy markets; Ito markets; semimartingale markets;
Other versions of this item:
- Constantinos Kardaras & Eckhard Platen, 2009. "Minimizing the expected market time to reach a certain wealth level," Papers 0904.1903, arXiv.org.
- NEP-ALL-2008-10-13 (All new papers)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Kardaras, Constantinos & Platen, Eckhard, 2011.
"On the semimartingale property of discounted asset-price processes,"
Stochastic Processes and their Applications,
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- Dirk Becherer, 2001. "The numeraire portfolio for unbounded semimartingales," Finance and Stochastics, Springer, vol. 5(3), pages 327-341.
- Eckhard Platen, 2004.
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- Constantinos Kardaras & Eckhard Platen, 2008. "On Financial Markets where only Buy-And-Hold Trading is Possible," Research Paper Series 213, Quantitative Finance Research Centre, University of Technology, Sydney.
- Eckhard Platen, 2009. "A Benchmark Approach to Investing and Pricing," Research Paper Series 253, Quantitative Finance Research Centre, University of Technology, Sydney.
- Zeng, Xudong, 2010. "Optimal reinsurance with a rescuing procedure," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 397-405, April.
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